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Popular Calculus Problems

integral of 4e^{5x}	\int\:4e^{5x}dx
integral of (3t-5)e^{2t}	\int\:(3t-5)e^{2t}dt
derivative of cos(sin(15e^x))	derivative\:\cos(\sin(15e^{x}))
integral of (x^2)/(sqrt(7+3x^3))	\int\:\frac{x^{2}}{\sqrt{7+3x^{3}}}dx
(\partial)/(\partial x)(e^{14xy})	\frac{\partial\:}{\partial\:x}(e^{14xy})
derivative of 3x^2-18x+24	\frac{d}{dx}(3x^{2}-18x+24)
sum from n=0 to infinity of 4+(-1)^n	\sum\:_{n=0}^{\infty\:}4+(-1)^{n}
integral from 0 to infinity of e^{-x-y}	\int\:_{0}^{\infty\:}e^{-x-y}dx
integral of e^{3x}(2x^2+1)	\int\:e^{3x}(2x^{2}+1)dx
tangent of x^2-4	tangent\:x^{2}-4
sum from n=1 to infinity of 1/((2n-1)^2)	\sum\:_{n=1}^{\infty\:}\frac{1}{(2n-1)^{2}}
integral from 6 to infinity of xe^{-3x}	\int\:_{6}^{\infty\:}xe^{-3x}dx
derivative of 1/3 x^3-x^2-3x+4	\frac{d}{dx}(\frac{1}{3}x^{3}-x^{2}-3x+4)
area 7x^4-7x^2,8x^2,0	area\:7x^{4}-7x^{2},8x^{2},0
(\partial)/(\partial y)(e^{-(x^2+y^2)})	\frac{\partial\:}{\partial\:y}(e^{-(x^{2}+y^{2})})
limit as x approaches 4 of ((ln(x)-ln(4)))/(x-4)	\lim\:_{x\to\:4}(\frac{(\ln(x)-\ln(4))}{x-4})
y^'=x^2y^2	y^{\prime\:}=x^{2}y^{2}
integral of (sin^2(x))/(cos(x))	\int\:\frac{\sin^{2}(x)}{\cos(x)}dx
derivative of f(x)=(x-5)/x	derivative\:f(x)=\frac{x-5}{x}
integral of x*arcsin(x^2)	\int\:x\cdot\:\arcsin(x^{2})dx
integral of t^9e^{-t^{10}}	\int\:t^{9}e^{-t^{10}}dt
integral from 1 to 4 of (2-x^2)-(6-5x)	\int\:_{1}^{4}(2-x^{2})-(6-5x)dx
derivative of (3x+4/(7x-5))	\frac{d}{dx}(\frac{3x+4}{7x-5})
tangent of (x^2-24)^6	tangent\:(x^{2}-24)^{6}
tangent of 5x^2+2x,\at x=3	tangent\:5x^{2}+2x,\at\:x=3
integral of sin^3(4θ)sqrt(cos(4θ))	\int\:\sin^{3}(4θ)\sqrt{\cos(4θ)}dθ
tangent of f(x)=x^2+4	tangent\:f(x)=x^{2}+4
(dy)/(dx)=(1+xy)/(1+x)	\frac{dy}{dx}=\frac{1+xy}{1+x}
(\partial)/(\partial y)(xsin(xy))	\frac{\partial\:}{\partial\:y}(x\sin(xy))
derivative of sin(2x-1)	\frac{d}{dx}(\sin(2x-1))
integral of-acos(x)	\int\:-a\cos(x)dx
derivative of arctan(x^3-1)	\frac{d}{dx}(\arctan(x^{3}-1))
(\partial)/(\partial x)(-2ye^{x^2-y^2})	\frac{\partial\:}{\partial\:x}(-2ye^{x^{2}-y^{2}})
taylor e^{-3x+1}+8	taylor\:e^{-3x+1}+8
integral of (e^{2t})/(e^{2t)-e^{-2t}}	\int\:\frac{e^{2t}}{e^{2t}-e^{-2t}}dt
(sin(x^2))^'	(\sin(x^{2}))^{\prime\:}
derivative of x-sin(pix)	derivative\:x-\sin(πx)
derivative of (x+8)^{1/3}	derivative\:(x+8)^{\frac{1}{3}}
integral of (x+2)^3	\int\:(x+2)^{3}dx
derivative of 2x^5e^x	\frac{d}{dx}(2x^{5}e^{x})
limit as x approaches 0+of x^2(1+ln(x))	\lim\:_{x\to\:0+}(x^{2}(1+\ln(x)))
derivative of f(x)= 2/(x^3)	derivative\:f(x)=\frac{2}{x^{3}}
derivative of cot^2(xpi)	derivative\:\cot^{2}(xπ)
derivative of y=6cos(x+y)	derivative\:y=6\cos(x+y)
integral of e^{8x+6}	\int\:e^{8x+6}dx
y^'=((cos(18x)))/((e^{(18*y)))}	y^{\prime\:}=\frac{(\cos(18x))}{(e^{(18\cdot\:y)})}
x^2y^{''}+3xy^'-3y=0	x^{2}y^{\prime\:\prime\:}+3xy^{\prime\:}-3y=0
dy-(y-9)^2dx=0	dy-(y-9)^{2}dx=0
derivative of x^{5/6}	derivative\:x^{\frac{5}{6}}
derivative of (x(2-x))/(e^x)	derivative\:\frac{x(2-x)}{e^{x}}
integral of 2ycos(y^2)	\int\:2y\cos(y^{2})dy
integral of (e^{1/x})/x	\int\:\frac{e^{\frac{1}{x}}}{x}dx
tangent of f(x)=sqrt(4x+65),(4,9)	tangent\:f(x)=\sqrt{4x+65},(4,9)
area y=sqrt(x),y=(x-3),(3,5.3)	area\:y=\sqrt{x},y=(x-3),(3,5.3)
(\partial)/(\partial y)(x^{1/2}y^{3/2})	\frac{\partial\:}{\partial\:y}(x^{\frac{1}{2}}y^{\frac{3}{2}})
integral from 0 to y^3 of xe^{-x/y}	\int\:_{0}^{y^{3}}xe^{-\frac{x}{y}}dx
integral of (24)/(1-cos(3x))	\int\:\frac{24}{1-\cos(3x)}dx
derivative of (2xsqrt(3x-1))/(5x)	derivative\:\frac{2x\sqrt{3x-1}}{5x}
integral of cot^5(2x)	\int\:\cot^{5}(2x)dx
integral of (4x^2-13x+12)/(x(x-2)^2)	\int\:\frac{4x^{2}-13x+12}{x(x-2)^{2}}dx
integral of (3x^3)/(sqrt(x^2+16))	\int\:\frac{3x^{3}}{\sqrt{x^{2}+16}}dx
derivative of (e^x/(cos(3x)))	\frac{d}{dx}(\frac{e^{x}}{\cos(3x)})
integral of cot^2(x)csc^2(x)	\int\:\cot^{2}(x)\csc^{2}(x)dx
integral of 7x^3e^{x^4}	\int\:7x^{3}e^{x^{4}}dx
derivative of (4x^2-5^3)	\frac{d}{dx}((4x^{2}-5)^{3})
xy^'-2y-8=0	xy^{\prime\:}-2y-8=0
derivative of f(x)=3x(18x^4+(13)/(x+1))	derivative\:f(x)=3x(18x^{4}+\frac{13}{x+1})
derivative of (6x^2+6x+6/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+6x+6}{\sqrt{x}})
derivative of 3^{2x}	derivative\:3^{2x}
(\partial)/(\partial x)(x^2+y^2-5)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-5)
(dy)/(dx)=sqrt(5y)e^{x+2}	\frac{dy}{dx}=\sqrt{5y}e^{x+2}
f(x)=sqrt(2x^2-7)	f(x)=\sqrt{2x^{2}-7}
integral from 0 to 1 of (2x)/((x^2+1)^2)	\int\:_{0}^{1}\frac{2x}{(x^{2}+1)^{2}}dx
area x= 1/2 y^2,y=1,y=-1/2 x+3	area\:x=\frac{1}{2}y^{2},y=1,y=-\frac{1}{2}x+3
(\partial)/(\partial y)((-y)/(y^2+x^2))	\frac{\partial\:}{\partial\:y}(\frac{-y}{y^{2}+x^{2}})
derivative of (3x-1/(sqrt(x^2+2)))	\frac{d}{dx}(\frac{3x-1}{\sqrt{x^{2}+2}})
derivative of sin(8cos(x))	\frac{d}{dx}(\sin(8\cos(x)))
integral of (tan^3(θ))/(cos^4(θ))	\int\:\frac{\tan^{3}(θ)}{\cos^{4}(θ)}dθ
xy^{''}+y^'=0	xy^{\prime\:\prime\:}+y^{\prime\:}=0
derivative of pi^{sqrt(x)}	\frac{d}{dx}(π^{\sqrt{x}})
(\partial}{\partial x}(\frac{sin(x))/x)	\frac{\partial\:}{\partial\:x}(\frac{\sin(x)}{x})
y^{''}-2y^'+10y=0,y(0)=4,y^'(0)=1	y^{\prime\:\prime\:}-2y^{\prime\:}+10y=0,y(0)=4,y^{\prime\:}(0)=1
limit as x approaches-9-of x^2+3/(x+9)	\lim\:_{x\to\:-9-}(x^{2}+\frac{3}{x+9})
(\partial)/(\partial y)((-y)/(2x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{-y}{2x^{2}+y^{2}})
derivative of (x-sqrt(x))/(x^{1/5)}	derivative\:\frac{x-\sqrt{x}}{x^{\frac{1}{5}}}
integral of (in(x))/(x^2)	\int\:\frac{in(x)}{x^{2}}dx
derivative of (3x/(4x-2))	\frac{d}{dx}(\frac{3x}{4x-2})
y^'+(7y)/(x+3)=(x+3)^3	y^{\prime\:}+\frac{7y}{x+3}=(x+3)^{3}
integral of t/((t^2+1)^{3/2)}	\int\:\frac{t}{(t^{2}+1)^{\frac{3}{2}}}dt
integral of (13x)/(x+3)	\int\:\frac{13x}{x+3}dx
limit as x approaches 2 of (5x-3)/4	\lim\:_{x\to\:2}(\frac{5x-3}{4})
integral of sqrt(25x^2-4)	\int\:\sqrt{25x^{2}-4}dx
integral of cos(θ)sin^8(θ)	\int\:\cos(θ)\sin^{8}(θ)dθ
integral of sqrt(2x)	\int\:\sqrt{2x}dx
integral of (e^x)/(e^{2x)+2e^x+1}	\int\:\frac{e^{x}}{e^{2x}+2e^{x}+1}dx
integral of 3/(y^3)	\int\:\frac{3}{y^{3}}dy
tangent of f(x)=x^2-4,\at 5	tangent\:f(x)=x^{2}-4,\at\:5
integral of xsin(x)	\int\:x\sin(x)dx
derivative of ln(1)	derivative\:\ln(1)
limit as x approaches infinity of 11/2	\lim\:_{x\to\:\infty\:}(\frac{11}{2})

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